Toast chiles on a clean baking sheet until slightly darkened, about 5 minutes. Let cool slightly, then remove stems, and seeds, if you prefer less heat. Place chiles, half of yellow onion, remaining garlic, and 1 cup hot water in a blender; let sit 10 minutes to soften chiles. Blend until smooth; set chile purée aside.

Heat oil in a large Dutch oven over medium-high heat. Working in batches, cook pork, turning occasionally, until browned, 8–10 minutes; transfer to a plate.

Pour off fat from pot. Cook chile purée in pot over medium-high heat, stirring occasionally, until reduced by half, 8–10 minutes. Add pork, oregano, remaining yellow onion, and 10 cups water to pot; season with salt and pepper. Bring to a boil, reduce heat, and simmer, partially covered, skimming occasionally, until pork is very tender, 3–3½ hours.

Add squash to stew and cook, uncovered, until pork is falling apart and squash is soft, 30–35 minutes; season with salt and pepper.

Reviews

This is a great recipe. It's pretty time consuming, but worth it in the end. The toppings are what makes this soup, DO NOT SKIP. I left the red onions in the lime juice for over an hour and it kind of was like a quick pickle. Perfect for a hot soup. I also served with lime wedges and cotija cheese. For the pepitas, I roasted them with some salt and honey to make them sweet. This was an impressive stew and tasted absolutely delicious.